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SLAC Publication: SLACPUB17251
SLAC Release Date: May 30, 2018
Singularity and Stability in a Periodic System of Particle Accelerators
Cai, Yunhai.
We study the singleparticle dynamics in a general and parameterized alternatinggradient cell with zero chromaticity using the Lie Algebra method. To our surprise, the firstorder perturbation of the sextupoles largely determines the dynamics away from the major resonances. The dynamic aperture can be estimated from the topology and geometry of the phase space. In the linearly normalized phase space, it is scaled according to, $\bar A \propto \phi\sqrt{L}$, where $\phi$ is the bending angle an... Show Full Abstract
We study the singleparticle dynamics in a general and parameterized alternatinggradient cell with zero chromaticity using the Lie Algebra method. To our surprise, the firstorder perturbation of the sextupoles largely determines the dynamics away from the major resonances. The dynamic aperture can be estimated from the topology and geometry of the phase space. In the linearly normalized phase space, it is scaled according to, $\bar A \propto \phi\sqrt{L}$, where $\phi$ is the bending angle and $L$ the length of the cell. For the two degrees of freedom with equal betatron tunes, the analytical perturbation theory leads us to the invariant or quasiinvariant tori, which play an important role in determining the stable volume in the fourdimensional phase space.
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